Functional triplet motifs underlie accurate predictions of single-trial responses in populations of tuned and untuned V1 neurons

Trial-by-trial variability in cortical responses exhibits scaling of spatial correlations predicted from critical dynamics

In the mammalian cortex, even simple sensory inputs or movements activate many neurons, with each neuron responding variably to repeated stimuli-a phenomenon known as trial-by-trial variability. Understanding the spatial patterns and dynamics of this variability is challenging. Using cellular 2-photon imaging, we study visual and auditory responses in the primary cortices of awake mice. We focus on how individual neurons' responses differed from the overall population. We find consistent spatial correlations in these differences that are unique to each trial and linearly scale with the cortical area observed, a characteristic of critical dynamics as confirmed in our neuronal simulations. Using chronic multi-electrode recordings, we observe similar scaling in the prefrontal and premotor cortex of non-human primates during self-initiated and visually cued motor tasks. These results suggest that trial-by-trial variability, rather than being random noise, reflects a critical, fluctuation-dominated state in the cortex, supporting the brain's efficiency in processing information.

Connecting the dots in the zona incerta: A study of neural assemblies and motifs of inter-area coordination in mice

The zona incerta (ZI), a subthalamic area connected to numerous brain regions, has raised clinical interest because its stimulation alleviates the motor symptoms of Parkinson's disease. To explore its coordinative nature, we studied the assembly formation in a dataset of neural recordings in mice and quantified the degree of functional coordination of ZI with other 24 brain areas. We found that the ZI is a highly integrative area. The analysis in terms of "loop-like" motifs, directional assemblies composed of three neurons spanning two areas, has revealed reciprocal functional interactions with reentrant signals that, in most cases, start and end with the activation of ZI units. In support of its proposed integrative role, we found that almost one-third of the ZI's neurons formed assemblies with more than half of the other recorded areas and that loop-like assemblies may stand out as hyper-integrative motifs compared to other types of activation patterns.

A dynamic subset of network interactions underlies tuning to natural movements in marmoset sensorimotor cortex

Mechanisms of computation in sensorimotor cortex must be flexible and robust to support skilled motor behavior. Patterns of neuronal coactivity emerge as a result of computational processes. Pairwise spike-time statistical relationships, across the population, can be summarized as a functional network (FN) which retains single-unit properties. We record populations of single-unit neural activity in forelimb sensorimotor cortex during prey-capture and spontaneous behavior and use an encoding model incorporating kinematic trajectories and network features to predict single-unit activity during forelimb movements. The contribution of network features depends on structured connectivity within strongly connected functional groups. We identify a context-specific functional group that is highly tuned to kinematics and reorganizes its connectivity between spontaneous and prey-capture movements. In the remaining context-invariant group, interactions are comparatively stable across behaviors and units are less tuned to kinematics. This suggests different roles in producing natural forelimb movements and contextualizes single-unit tuning properties within population dynamics.

Normalization in mouse primary visual cortex

When multiple stimuli appear together in the receptive field of a visual cortical neuron, the response is typically close to the average of that neuron's response to each individual stimulus. The departure from a linear sum of each individual response is referred to as normalization. In mammals, normalization has been best characterized in the visual cortex of macaques and cats. Here we study visually evoked normalization in the visual cortex of awake mice using imaging of calcium indicators in large populations of layer 2/3 (L2/3) V1 excitatory neurons and electrophysiological recordings across layers in V1. Regardless of recording method, mouse visual cortical neurons exhibit normalization to varying degrees. The distributions of normalization strength are similar to those described in cats and macaques, albeit slightly weaker on average.

Dynamic structure of motor cortical neuron coactivity carries behaviorally relevant information

Skillful, voluntary movements are underpinned by computations performed by networks of interconnected neurons in the primary motor cortex (M1). Computations are reflected by patterns of coactivity between neurons. Using pairwise spike time statistics, coactivity can be summarized as a functional network (FN). Here, we show that the structure of FNs constructed from an instructed-delay reach task in nonhuman primates is behaviorally specific: Low-dimensional embedding and graph alignment scores show that FNs constructed from closer target reach directions are also closer in network space. Using short intervals across a trial, we constructed temporal FNs and found that temporal FNs traverse a low-dimensional subspace in a reach-specific trajectory. Alignment scores show that FNs become separable and correspondingly decodable shortly after the Instruction cue. Finally, we observe that reciprocal connections in FNs transiently decrease following the Instruction cue, consistent with the hypothesis that information external to the recorded population temporarily alters the structure of the network at this moment.

A transthalamic pathway crucial for perception

Perception arises from activity between cortical areas, first primary cortex and then higher order cortices. This communication is served in part by transthalamic (cortico-thalamo-cortical) pathways, which ubiquitously parallel direct corticocortical pathways, but their role in sensory processing has largely remained unexplored. Here, we show that the transthalamic pathway linking somatosensory cortices propagates task-relevant information required for correct sensory decisions. Using optogenetics, we specifically inhibited the pathway at its synapse in higher order somatosensory thalamus of mice performing a texture-based discrimination task. We concurrently monitored the cellular effects of inhibition in primary or secondary cortex using two-photon calcium imaging. Inhibition severely impaired performance despite intact direct corticocortical projections, thus challenging the purely corticocentric map of perception. Interestingly, the inhibition did not reduce overall cell responsiveness to texture stimulation in somatosensory cortex, but rather disrupted the texture selectivity of cells, a discriminability that develops over task learning. This discriminability was more disrupted in the secondary than primary somatosensory cortex, emphasizing the feedforward influence of the transthalamic route. Transthalamic pathways thus appear critical in delivering performance-relevant information to higher order cortex and are critical hierarchical pathways in perceptual decision-making.

Normalization in mouse primary visual cortex

When multiple stimuli appear together in the receptive field of a visual cortical neuron, the response is typically close to the average of that neuron's response to each individual stimulus. The departure from a linear sum of each individual response is referred to as normalization. In mammals, normalization has been best characterized in the visual cortex of macaques and cats. Here we study visually evoked normalization in the visual cortex of awake mice using optical imaging of calcium indicators in large populations of layer 2/3 (L2/3) V1 excitatory neurons and electrophysiological recordings across layers in V1. Regardless of recording method, mouse visual cortical neurons exhibit normalization to varying degrees. The distributions of normalization strength are similar to those described in cats and macaques, albeit slightly weaker on average.

Third-order motifs are sufficient to fully and uniquely characterize spatiotemporal neural network activity

Neuroscientific analyses balance between capturing the brain's complexity and expressing that complexity in meaningful and understandable ways. Here we present a novel approach that fully characterizes neural network activity and does so by uniquely transforming raw signals into easily interpretable and biologically relevant metrics of network behavior. We first prove that third-order (triple) correlation describes network activity in its entirety using the triple correlation uniqueness theorem. Triple correlation quantifies the relationships among three events separated by spatial and temporal lags, which are triplet motifs. Classifying these motifs by their event sequencing leads to fourteen qualitatively distinct motif classes that embody well-studied network behaviors including synchrony, feedback, feedforward, convergence, and divergence. Within these motif classes, the summed triple correlations provide novel metrics of network behavior, as well as being inclusive of commonly used analyses. We demonstrate the power of this approach on a range of networks with increasingly obscured signals, from ideal noiseless simulations to noisy experimental data. This approach can be easily applied to any recording modality, so existing neural datasets are ripe for reanalysis. Triple correlation is an accessible signal processing tool with a solid theoretical foundation capable of revealing previously elusive information within recordings of neural networks.

A deep learning framework for inference of single-trial neural population dynamics from calcium imaging with subframe temporal resolution

In many areas of the brain, neural populations act as a coordinated network whose state is tied to behavior on a millisecond timescale. Two-photon (2p) calcium imaging is a powerful tool to probe such network-scale phenomena. However, estimating the network state and dynamics from 2p measurements has proven challenging because of noise, inherent nonlinearities and limitations on temporal resolution. Here we describe Recurrent Autoencoder for Discovering Imaged Calcium Latents (RADICaL), a deep learning method to overcome these limitations at the population level. RADICaL extends methods that exploit dynamics in spiking activity for application to deconvolved calcium signals, whose statistics and temporal dynamics are quite distinct from electrophysiologically recorded spikes. It incorporates a new network training strategy that capitalizes on the timing of 2p sampling to recover network dynamics with high temporal precision. In synthetic tests, RADICaL infers the network state more accurately than previous methods, particularly for high-frequency components. In 2p recordings from sensorimotor areas in mice performing a forelimb reach task, RADICaL infers network state with close correspondence to single-trial variations in behavior and maintains high-quality inference even when neuronal populations are substantially reduced.

Edges in brain networks: Contributions to models of structure and function

Network models describe the brain as sets of nodes and edges that represent its distributed organization. So far, most discoveries in network neuroscience have prioritized insights that highlight distinct groupings and specialized functional contributions of network nodes. Importantly, these functional contributions are determined and expressed by the web of their interrelationships, formed by network edges. Here, we underscore the important contributions made by brain network edges for understanding distributed brain organization. Different types of edges represent different types of relationships, including connectivity and similarity among nodes. Adopting a specific definition of edges can fundamentally alter how we analyze and interpret a brain network. Furthermore, edges can associate into collectives and higher order arrangements, describe time series, and form edge communities that provide insights into brain network topology complementary to the traditional node-centric perspective. Focusing on the edges, and the higher order or dynamic information they can provide, discloses previously underappreciated aspects of structural and functional network organization.

Bridging neuronal correlations and dimensionality reduction

Two commonly used approaches to study interactions among neurons are spike count correlation, which describes pairs of neurons, and dimensionality reduction, applied to a population of neurons. Although both approaches have been used to study trial-to-trial neuronal variability correlated among neurons, they are often used in isolation and have not been directly related. We first established concrete mathematical and empirical relationships between pairwise correlation and metrics of population-wide covariability based on dimensionality reduction. Applying these insights to macaque V4 population recordings, we found that the previously reported decrease in mean pairwise correlation associated with attention stemmed from three distinct changes in population-wide covariability. Overall, our work builds the intuition and formalism to bridge between pairwise correlation and population-wide covariability and presents a cautionary tale about the inferences one can make about population activity by using a single statistic, whether it be mean pairwise correlation or dimensionality.

Partial information decomposition reveals that synergistic neural integration is greater downstream of recurrent information flow in organotypic cortical cultures

The directionality of network information flow dictates how networks process information. A central component of information processing in both biological and artificial neural networks is their ability to perform synergistic integration–a type of computation. We established previously that synergistic integration varies directly with the strength of feedforward information flow. However, the relationships between both recurrent and feedback information flow and synergistic integration remain unknown. To address this, we analyzed the spiking activity of hundreds of neurons in organotypic cultures of mouse cortex. We asked how empirically observed synergistic integration–determined from partial information decomposition–varied with local functional network structure that was categorized into motifs with varying recurrent and feedback information flow. We found that synergistic integration was elevated in motifs with greater recurrent information flow beyond that expected from the local feedforward information flow. Feedback information flow was interrelated with feedforward information flow and was associated with decreased synergistic integration. Our results indicate that synergistic integration is distinctly influenced by the directionality of local information flow.

Networks compute information. That is, they modify inputs to generate distinct outputs. These computations are an important component of network information processing. Knowing how the routing of information in a network influences computation is therefore crucial. Here we asked how a key form of computation—synergistic integration—is related to the direction of local information flow in networks of spiking cortical neurons. Specifically, we asked how information flow between input neurons (i.e., recurrent information flow) and information flow from output neurons to input neurons (i.e., feedback information flow) was related to the amount of synergistic integration performed by output neurons. We found that greater synergistic integration occurred where there was more recurrent information flow. And, lesser synergistic integration occurred where there was more feedback information flow relative to feedforward information flow. These results show that computation, in the form of synergistic integration, is distinctly influenced by the directionality of local information flow. Such work is valuable for predicting where and how network computation occurs and for designing networks with desired computational abilities.

Cyclic transitions between higher order motifs underlie sustained asynchronous spiking in sparse recurrent networks

A basic—yet nontrivial—function which neocortical circuitry must satisfy is the ability to maintain stable spiking activity over time. Stable neocortical activity is asynchronous, critical, and low rate, and these features of spiking dynamics contribute to efficient computation and optimal information propagation. However, it remains unclear how neocortex maintains this asynchronous spiking regime. Here we algorithmically construct spiking neural network models, each composed of 5000 neurons. Network construction synthesized topological statistics from neocortex with a set of objective functions identifying naturalistic low-rate, asynchronous, and critical activity. We find that simulations run on the same topology exhibit sustained asynchronous activity under certain sets of initial membrane voltages but truncated activity under others. Synchrony, rate, and criticality do not provide a full explanation of this dichotomy. Consequently, in order to achieve mechanistic understanding of sustained asynchronous activity, we summarized activity as functional graphs where edges between units are defined by pairwise spike dependencies. We then analyzed the intersection between functional edges and synaptic connectivity- i.e. recruitment networks. Higher-order patterns, such as triplet or triangle motifs, have been tied to cooperativity and integration. We find, over time in each sustained simulation, low-variance periodic transitions between isomorphic triangle motifs in the recruitment networks. We quantify the phenomenon as a Markov process and discover that if the network fails to engage this stereotyped regime of motif dominance “cycling”, spiking activity truncates early. Cycling of motif dominance generalized across manipulations of synaptic weights and topologies, demonstrating the robustness of this regime for maintenance of network activity. Our results point to the crucial role of excitatory higher-order patterns in sustaining asynchronous activity in sparse recurrent networks. They also provide a possible explanation why such connectivity and activity patterns have been prominently reported in neocortex.

Neocortical spiking activity tends to be low-rate and non-rhythmic, and to operate near the critical point of a phase transition. It remains unclear how this kind of spiking activity can be maintained within a neuronal network. Neurons are leaky and individual synaptic connections are sparse and weak, making the maintenance of an asynchronous regime a nontrivial problem. Higher order patterns involving more than two units abound in neocortex, and several lines of evidence suggest that they may be instrumental for brain function. For example, stable activity in vivo displays elevated clustering dominated by specific three-node (triplet) motifs. In this study we demonstrate a link between the maintenance of asynchronous activity and triplet motifs. We algorithmically build spiking neural network models to mimic the topology of neocortex and the spiking statistics that characterize wakefulness. We show that higher order coordination of synapses is always present during sustained asynchronous activity. Coordination takes the form of transitions in time between specific triangle motifs. These motifs summarize the way spikes traverse the underlying synaptic topology. The results of our model are consistent with numerous experimental observations, and their generalizability to other weakly and sparsely connected networks is predicted.

Autonomous emergence of connectivity assemblies via spike triplet interactions

Non-random connectivity can emerge without structured external input driven by activity-dependent mechanisms of synaptic plasticity based on precise spiking patterns. Here we analyze the emergence of global structures in recurrent networks based on a triplet model of spike timing dependent plasticity (STDP), which depends on the interactions of three precisely-timed spikes, and can describe plasticity experiments with varying spike frequency better than the classical pair-based STDP rule. We derive synaptic changes arising from correlations up to third-order and describe them as the sum of structural motifs, which determine how any spike in the network influences a given synaptic connection through possible connectivity paths. This motif expansion framework reveals novel structural motifs under the triplet STDP rule, which support the formation of bidirectional connections and ultimately the spontaneous emergence of global network structure in the form of self-connected groups of neurons, or assemblies. We propose that under triplet STDP assembly structure can emerge without the need for externally patterned inputs or assuming a symmetric pair-based STDP rule common in previous studies. The emergence of non-random network structure under triplet STDP occurs through internally-generated higher-order correlations, which are ubiquitous in natural stimuli and neuronal spiking activity, and important for coding. We further demonstrate how neuromodulatory mechanisms that modulate the shape of the triplet STDP rule or the synaptic transmission function differentially promote structural motifs underlying the emergence of assemblies, and quantify the differences using graph theoretic measures.

Emergent non-random connectivity structures in different brain regions are tightly related to specific patterns of neural activity and support diverse brain functions. For instance, self-connected groups of neurons, known as assemblies, have been proposed to represent functional units in brain circuits and can emerge even without patterned external instruction. Here we investigate the emergence of non-random connectivity in recurrent networks using a particular plasticity rule, triplet STDP, which relies on the interaction of spike triplets and can capture higher-order statistical dependencies in neural activity. We derive the evolution of the synaptic strengths in the network and explore the conditions for the self-organization of connectivity into assemblies. We demonstrate key differences of the triplet STDP rule compared to the classical pair-based rule in terms of how assemblies are formed, including the realistic asymmetric shape and influence of novel connectivity motifs on network plasticity driven by higher-order correlations. Assembly formation depends on the specific shape of the STDP window and synaptic transmission function, pointing towards an important role of neuromodulatory signals on formation of intrinsically generated assemblies.

Network Analysis of Murine Cortical Dynamics Implicates Untuned Neurons in Visual Stimulus Coding

Unbiased and dense sampling of large populations of layer 2/3 pyramidal neurons in mouse primary visual cortex (V1) reveals two functional sub-populations: neurons tuned and untuned to drifting gratings. Whether functional interactions between these two groups contribute to the representation of visual stimuli is unclear. To examine these interactions, we summarize the population partial pairwise correlation structure as a directed and weighted graph. We find that tuned and untuned neurons have distinct topological properties, with untuned neurons occupying central positions in functional networks (FNs). Implementation of a decoder that utilizes the topology of these FNs yields accurate decoding of visual stimuli. We further show that decoding performance degrades comparably following manipulations of either tuned or untuned neurons. Our results demonstrate that untuned neurons are an integral component of V1 FNs and suggest that network interactions contain information about the stimulus that is accessible to downstream elements.

Dynamic Tracking Algorithm for Time-Varying Neuronal Network Connectivity using Wide-Field Optical Image Video Sequences

Propagation of signals between neurons and brain regions provides information about the functional properties of neural networks, and thus information transfer. Advances in optical imaging and statistical analyses of acquired optical signals have yielded various metrics for inferring neural connectivity, and hence for mapping signal intercorrelation. However, a single coefficient is traditionally derived to classify the connection strength between two cells, ignoring the fact that neural systems are inherently time-variant systems. To overcome these limitations, we utilized a time-varying Pearson's correlation coefficient, spike-sorting, wavelet transform, and wavelet coherence of calcium transients from DIV 12-15 hippocampal neurons from GCaMP6s mice after applying various concentrations of glutamate. Results provide a comprehensive overview of resulting firing patterns, network connectivity, signal directionality, and network properties. Together, these metrics provide a more comprehensive and robust method of analyzing transient neural signals, and enable future investigations for tracking the effects of different stimuli on network properties.

Recurrent interactions can explain the variance in single trial responses

To develop a complete description of sensory encoding, it is necessary to account for trial-to-trial variability in cortical neurons. Using a linear model with terms corresponding to the visual stimulus, mouse running speed, and experimentally measured neuronal correlations, we modeled short term dynamics of L2/3 murine visual cortical neurons to evaluate the relative importance of each factor to neuronal variability within single trials. We find single trial predictions improve most when conditioning on the experimentally measured local correlations in comparison to predictions based on the stimulus or running speed. Specifically, accurate predictions are driven by positively co-varying and synchronously active functional groups of neurons. Including functional groups in the model enhances decoding accuracy of sensory information compared to a model that assumes neuronal independence. Functional groups, in encoding and decoding frameworks, provide an operational definition of Hebbian assemblies in which local correlations largely explain neuronal responses on individual trials.

Methamphetamine regulation of activity and topology of ventral midbrain networks

The ventral midbrain supports a variety of functions through the heterogeneity of neurons. Dopaminergic and GABA neurons within this region are particularly susceptible targets of amphetamine-class psychostimulants such as methamphetamine. While this has been evidenced through single-neuron methods, it remains unclear whether and to what extent the local neuronal network is affected and if so, by which mechanisms. Both GABAergic and dopaminergic neurons were heavily featured within the primary ventral midbrain network model system. Using spontaneous calcium activity, our data suggest methamphetamine decreased total network output via a D2 receptor-dependent manner. Over culture duration, functional connectivity between neurons decreased significantly but was unaffected by methamphetamine. However, across culture duration, exposure to methamphetamine significantly altered changes in network assortativity. Here we have established primary ventral midbrain networks culture as a viable model system that reveals specific changes in network activity, connectivity, and topology modulation by methamphetamine. This network culture system enables control over the type and number of neurons that comprise a network and facilitates detection of emergent properties that arise from the specific organization. Thus, the multidimensional properties of methamphetamine can be unraveled, leading to a better understanding of its impact on the local network structure and function.

Neuronal Avalanches in Input and Associative Layers of Auditory Cortex

The primary auditory cortex processes acoustic sequences for the perception of behaviorally meaningful sounds such as speech. Sound information arrives at its input layer four from where activity propagates to associative layer 2/3. It is currently not known whether there is a characteristic organization of neuronal population activity across layers and sound levels during sound processing. Here, we identify neuronal avalanches, which in theory and experiments have been shown to maximize dynamic range and optimize information transfer within and across networks, in primary auditory cortex. We used in vivo 2-photon imaging of pyramidal neurons in cortical layers L4 and L2/3 of mouse A1 to characterize the populations of neurons that were active spontaneously, i.e., in the absence of a sound stimulus, and those recruited by single-frequency tonal stimuli at different sound levels. Single-frequency sounds recruited neurons of widely ranging frequency selectivity in both layers. We defined neuronal ensembles as neurons being active within or during successive temporal windows at the temporal resolution of our imaging. For both layers, neuronal ensembles were highly variable in size during spontaneous activity as well as during sound presentation. Ensemble sizes distributed according to power laws, the hallmark of neuronal avalanches, and were similar across sound levels. Avalanches activated by sound were composed of neurons with diverse tuning preference, yet with selectivity independent of avalanche size. Our results suggest that optimization principles identified for avalanches guide population activity in L4 and L2/3 of auditory cortex during and in-between stimulus processing.

Reducing the Effect of Spurious Phase Variations in Neural Oscillatory Signals

The phase-reset model of oscillatory EEG activity has received a lot of attention in the last decades for decoding different cognitive processes. Based on this model, the ERPs are assumed to be generated as a result of phase reorganization in ongoing EEG. Alignment of the phase of neuronal activities can be observed within or between different assemblies of neurons across the brain. Phase synchronization has been used to explore and understand perception, attentional binding and considering it in the domain of neuronal correlates of consciousness. The importance of the topic and its vast exploration in different domains of the neuroscience presses the need for appropriate tools and methods for measuring the level of phase synchronization of neuronal activities. Measuring the level of instantaneous phase (IP) synchronization has been used extensively in numerous studies of ERPs as well as oscillatory activity for a better understanding of the underlying cognitive binding with regard to different set of stimulations such as auditory and visual. However, the reliability of results can be challenged as a result of noise artifact in IP. Phase distortion due to environmental noise artifacts as well as different pre-processing steps on signals can lead to generation of artificial phase jumps. One of such effects presented recently is the effect of low envelope on the IP of signal. It has been shown that as the instantaneous envelope of the analytic signal approaches zero, the variations in the phase increase, effectively leading to abrupt transitions in the phase. These abrupt transitions can distort the phase synchronization results as they are not related to any neurophysiological effect. These transitions are called spurious phase variation. In this study, we present a model to remove generated artificial phase variations due to the effect of low envelope. The proposed method is based on a simplified form of a Kalman smoother, that is able to model the IP behavior in narrow-bandpassed oscillatory signals. In this work we first explain the details of the proposed Kalman smoother for modeling the dynamics of the phase variations in narrow-bandpassed signals and then evaluate it on a set of synthetic signals. Finally, we apply the model on ongoing-EEG signals to assess the removal of spurious phase variations.